Simultaneous Confidence Limits for Cross-Product Ratios in Contingency Tables
列联表交叉乘积比的同时置信限AI 解读 ↓
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列联表交叉乘积比的同时置信限
- 研究问题
- 如何简化列联表交叉乘积比的区间计算，并对较大列联表中的多个比值及跨表相对差异构造同时置信区间？
- 方法与思路
- 作者提出较简便的置信限构造，推广到一般列联表和多表比较，并修改及扩展既有的二乘二表方法。
- 材料陈述的贡献
- 摘要称二乘二表区间与既有方法渐近等价；较大维度下，在通常概率水平上，所述同时区间渐近更短。
- 阅读关注点
- 应核对抽样方案、同时覆盖的控制方式、跨表相对差异的定义，以及区间长度比较所需的维度和概率条件。
- 阅读边界
- 仅据 Crossref 所供摘要，未核验其他版本；渐近更短不等于有限样本覆盖更好，具体条件与数值表现未提供。
原文摘要
Summary Fisher (1962) has proposed a method for obtaining confidence limits for the cross-product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits for the cross-product ratio in a 2 × 2 table, and we shall extend these methods to obtain simultaneous confidence intervals for the r(r - 1) c(c - l)/4 cross-product ratios in an r × c table (or for a subset of them) and also for the relative differences between the corresponding cross-product ratios in K different r × c tables. In addition, we shall present a modification of a method suggested by Gart (1962a) for the 2 × 2 table, and we shall extend the modified method to the r × c table. The methods presented herein are easier to apply than those given in the earlier literature. For the 2 × 2 table, the confidence limits presented herein are asymptotically equivalent to the limits given earlier. When max (r, c, K) > 2, the simultaneous confidence intervals presented herein for the cross-product ratios and for the relative differences between cross-product ratios are asymptotically shorter than the corresponding intervals given by Cornfield (1956), for the usual probability levels. The method proposed herein for studying the relative differences between cross-product ratios in K r × c tables can also be used to supplement the earlier methods of analysis given by Plackett (1962) and Goodman (1963b) for testing the null hypothesis that these differences are all nil.